Coastguard's 27° angle to first ship, 750m behind which lies second, yields second ship's angle around 11°. (Visualize triangle with labelled points and angles)
1. Define the situation:
Imagine a triangle representing the scenario:
Point A: The coastguard at 240 meters above sea level.
Point B: The first ship (distance unknown).
Point C: The second ship 750 meters behind the first ship.
Angle α: The angle of depression from the coastguard to the first ship (given as 27°).
2. Use trigonometry:
Since we have a right triangle (ABC) with one angle (α) and one side length (AC = 240 m) known, we can use trigonometry (specifically, the tangent function) to find the missing side lengths.
3. Find the distance to the first ship (AB):
tan(α) = AC / AB
tan(27°) = 240 m / AB
AB ≈ 535 meters (using the tangent ratio table or calculator)
4. Find the distance to the second ship (BC):
BC = AB + 750 m
BC = 535 m + 750 m
BC = 1285 meters
5. Calculate the angle to the second ship (β):
tan(β) = AC / BC
tan(β) = 240 m / 1285 m
β ≈ 10.6° (using the tangent ratio table or calculator)
6. Round to the nearest degree:
The angle of depression to the second ship is approximately 11° (rounded to the nearest degree).
Therefore, the coastguard would measure an angle of depression of 11° to the second ship.
Note: This solution assumes the Earth is flat for simplicity of calculations. In reality, Earth's curvature would introduce a slight difference in the actual angle.